The PUBG Test Server download process is fairly easy. PUBG Corp uses the test server to implement new changes, try out patch changes and generally test the game before a new update.
But not everyone can use the test server at launch. Despite owning the base game, you need to download the test server if you want to participate.
PUBG Test Server Download: How to Download on Xbox
It's a bit different for PC and console players, but Xbox One and PlayStation 4 owners will do the same thing. For PC players, head to the Steam Library and look up PUBG. You'll find the base game which you already own, but underneath it is PUBG Test Server for free.
For console players, head to your specific store and look up PUBG PTS. It's also free to download. Once you have it downloaded, restart your console or PC, and you'll be free to join the server. Try out new things like Patch 6.1 and additions like the Sticky Bomb.